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ABSTRACT

ABSTRACT
If the Hamiltonian is a bounded selfadjoint operator, we give a simple alternative characterization of the infinitesimal generator iC of the unitary group associated with a Quantum Stochastic Differential Equation (QSDE). By using the defect indices of the symmetric operator C, we give a sufficient condition that assures that iC is the restriction of a generator of a strongly continuous semigroup of isometries in the case when the Hamiltonian is an unbounded symmetric operator.

ABSTRACT

ABSTRACT
We consider a model of electrical conductivity in a lattice deduced by L. Accardi and S. Kozyrev from the stochastic limit of a general system of spins interacting with a boson field. We search for diagonal (or classical) invariant states of the associated Quantum Markov Semigroup and show that: a) They correspond with invariant measures of a classical asymmetric exclusion process. b) Associated with every energy function, there exists infinitely many invariant states. c) Any element in the closed convex hull of the above states satisfies a quantum detailed balance condition. d) Any initial state is driven by the asymmetric exclusion QMS to an equilibrium state.